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a(1) = 1, then group the natural numbers so that the n-th group contains n numbers relatively prime to n whose sum is divisible by n.
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%I #13 Sep 23 2023 03:10:58

%S 1,3,5,2,8,11,7,9,13,15,4,6,12,14,19,17,23,25,29,31,37,10,16,18,20,22,

%T 24,30,21,27,33,35,39,41,43,49,26,28,32,34,38,40,44,47,53,51,57,59,61,

%U 63,67,69,71,73,79,36,42,45,46,48,50,52,54,56,58,74,55,65,77,83,85,89

%N a(1) = 1, then group the natural numbers so that the n-th group contains n numbers relatively prime to n whose sum is divisible by n.

%e Triangle begins:

%e 1;

%e 3, 5;

%e 2, 8, 11;

%e 7, 9, 13, 15;

%e 4, 6, 12, 14, 19;

%e 17, 23, 25, 29, 31, 37;

%e ...

%e T(3, 2) is 8 because if it were 4 or 7, we could not add a number relatively prime to 3 and get a sum divisible by 3.

%o (PARI) print1(1, " "); used = vector(10000); used[1] = 1; x = 2; for (n = 2, 15, i = x; s = 0; for (k = 1, n - 2, while (used[i] || gcd(i, n) > 1, i++); print1(i, " "); used[i] = 1; s += i; i++); while (used[i] || gcd(i, n) > 1 || gcd(i + s, n) > 1, i++); print1(i, " "); used[i] = 1; s += i; i += (n - (i + s)%n); while (used[i], i += n); print1(i, " "); used[i] = 1; while (used[x], x++)); \\ _David Wasserman_, Jan 22 2005

%Y Cf. A075627, A075628, A075629, A075630.

%K nonn,tabl

%O 1,2

%A _Amarnath Murthy_, Sep 30 2002

%E More terms from _David Wasserman_, Jan 22 2005